1st Edition
Multiplicative Differential Equations Volume II
Multiplicative Differential Equations: Volume II is the second part of a comprehensive approach to the subject. It continues a series of books written by the authors on multiplicative, geometric approaches to key mathematical topics. This volume is devoted to the theory of multiplicative differential systems. The asymptotic behavior of the solutions of such systems is studied. Stability theory for multiplicative linear and nonlinear systems is introduced and boundary value problems for second-order multiplicative linear and nonlinear equations are explored. The authors also present first-order multiplicative partial differential equations. Each chapter ends with a section of practical problems. The text is accessible to graduate students and researchers in mathematics, physics, engineering and biology.
Preface
1 Systems Multiplicative Differential Equations
1.1 Systems of Multiplicative Linear Differential Equations
1.2 nth Order MDE
1.3 Multiplicative Homogeneous Systems
1.4 Multiplicative Fundamental Matrix Solutions
1.5 Multiplicative Adjoint Systems
1.6 The Method of Variation of Constants
1.7 Systems with Multiplicative Constant Coefficients
1.8 Advanced Practical Exercises
2 Qualitative Analysis of Multiplicative Differential Systems
2.1 Periodic Multiplicative Linear Systems
2.2 Asymptotic Behaviour of Solutions I
2.3 Asymptotic Behaviour of Solutions II
2.4 Asymptotic Behaviour of Solutions III
2.5 Asymptotic Behaviour of Solutions IV
2.6 Asymptotic Behaviour of Solutions V
2.7 Asymptotic Behaviour of Solutions VI
2.8 Advanced Practical Problems
3 Stability Theory
3.1 Definition. Examples
3.2 Criteria for Stability
3.3 Uniform Stability
3.4 Stability of Quasi-Multiplicative Linear Systems
3.5 Two-Dimensional Autonomous Systems
3.6 Advanced Practical Problems
4 Multiplicative Linear Boundary Value Problems
4.1 Introduction
4.2 Existence of Solution
4.3 Multiplicative Green Functions
4.4 Advanced Practical Problems
5 Multiplicative Nonlinear MDEs
5.1 Multiplicative Lyapunov Direct Method I
5.2 Multiplicative Lyapunov Direct Method II
5.3 Multiplicative Nonlinear BVPs
5.4 Advanced Practical Problems
6 First Order MPDE
6.1 Classification
6.2 Solvability
6.3 The Cauchy Problem
6.4 The Multiplicative Pfaff Equation
6.5 Some Special Systems
6.6 Advanced Practical Problems
Bibliography
Index
Biography
Svetlin G. Georgiev (born 05 April 1974, Rouse, Bulgaria) is a mathematician who has worked in various areas of mathematics. He currently focuses on harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, integral equations and dynamic calculus on time scales.
Khaled Zennir was born in Skikda, Algeria, in 1982. He received his PhD in Mathematics in 2013 from Sidi Bel Abbès University, Algeria (Assist. Professor). He obtained his highest diploma in Algeria (Habilitation, Mathematics) from Constantine University, Algeria, in May 2015 (Assoc. Professor). He is now Associate Professor at Qassim University, KSA. His research interests lie in nonlinear hyperbolic partial differential equations: global existence, blow-up and long time behavior.
